1. For the countries shown, the correlation between median days and total instructional

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1. For the countries shown, (a) the correlation between median days and total instructional

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hours is very slightly negative (about - 0.0068), the correlation between median days and math scores is slightly positive (about + 0.1083), and the correlation between total instructional hours and math scores is moderately negative (about - 0.3969). Are any, or all, of these correlations surprising?<br>

+

hours is very slightly negative (about - 0.0068), (b) the correlation between median days and math scores is slightly positive (about + 0.1083), and (c) the correlation between total instructional hours and math scores is moderately negative (about - 0.3969). Are any, or all, of these correlations surprising?<br>

2. From this data alone, could you conclude that extending the U.S. school year or school day would improve math scores?<br>

2. From this data alone, could you conclude that extending the U.S. school year or school day would improve math scores?<br>

3. What information, behind this data, might you need in order to draw any conclusions about the effect of an extended school year or a school day on math scores in any country?<br>

3. What information, behind this data, might you need in order to draw any conclusions about the effect of an extended school year or a school day on math scores in any country?<br>

Revision as of 15:01, 21 January 2011

Contents

Quotations

"The interpretation of statistical signiﬁcance tests is liable to a misconception known
as the fallacy of the transposed conditional. In this fallacy, the probability of the data
given a hypothesis (e.g., P(D|H), such as the probability of someone being dead given that
they were lynched, a probability that is close to 1) is confused with the probability of the
hypothesis given the data (e.g., P(H|D), such as the probability that someone was lynched
given that they are dead, a probability that is close to zero)."

We reanalyze Bem’s data using a default Bayesian t-test and show that the evidence for psi ["ESP"] is weak to nonexistent. …. We conclude that Bem’s p-values do not indicate evidence in favor of precognition; instead, they indicate that experimental psychologists need to change the way they conduct their experiments and analyze their data.

Submitted by Margaret Cibes based on an ISOSTAT posting by Randall Pruim

Placebos without deception

Although somewhat of an exaggeration, before the invention of aspirin, MDs had nothing to offer except placebos. Today, no study in the medical field can be taken seriously without a control for the so-called placebo effect. In an unusual twist whereby the placebo is the treatment, Kaptchuk, et al openly beforehand informed 37 patients suffering from irritable bowl syndrome (IBS) that they were receiving a placebo “without any medication in it.” The other 43 patients were a control, i.e., no treatment, in that they received no medication whatsoever.

The Globe article put it this way:

The researchers got some astounding results when they gave placebos — gelatin capsules filled with nondigestible cellulose — to patients suffering from irritable bowel syndrome for three weeks. Nearly 60 percent reported an improvement in their symptoms compared with 35 percent of the patients who took nothing beyond their usual treatments.
But here is the kicker: The placebo takers knew they were popping the equivalent of sugar pills, yet they still said they experienced less abdominal pain, constipation, or loose stools during the study.

Discussion

1. Here is the
table of treatment outcomes from the Kaptchuk paper and an associated graphic (the phrase “Open Placebo” means no deception). Use a statistics package to verify the p-values given there.

2. Just to confuse things now that the power of the placebo has been firmly established for IBS, consider this which also was recently published:

In two studies involving more than 1,200 subjects with diarrhea-predominant IBS, researchers found that a two-week course of the antibiotic rifaximin helped relieve symptoms not only during treatment, but also for weeks after the medication was stopped.

Participants who were randomly assigned to receive the drug reported less bloating and abdominal pain, and improved stool consistency for up to 10 weeks, say the authors, whose paper is published in this week's New England Journal of Medicine.

About 40 per cent or more of subjects given the thrice-daily rifaximin pill had significantly diminished IBS symptoms compared to those given placebo, or dummy pills, the study found.

Dr. Lawrence Cohen who was not involved with the study

said rifaximin could have potential, although how much is difficult to determine because the difference in the proportion of those reporting symptom relief in the study's treated group versus the placebo group wasn't that dramatic.

"It's statistically significant, yes. But is it clinically significant?"

While the findings shouldn't be dismissed, Cohen said he is cautious about the study because it was designed and funded by rifaximin's maker, Salix Pharmaceuticals Inc., a fact disclosed by the researchers. Pimentel [director of the Gastrointestinal Motility Program at Cedars-Sinai Medical Center] discovered the use of rifaximin for IBS, and Cedars-Sinai holds patent rights to this discovery and has licensed those rights to Salix.

Submitted by Paul Alper

Go figure, go finger

Times are hard and academics need to publish in an environment in which not a great deal of money is available for gathering data. A popular way to do things inexpensively and create a stir in the lay press is to look at finger lengths. Previous Chance News wikis on the subject of finger lengths may be found here and here.

In the present article, Tim Dowling comments on the more unusual past claims put forward in academic journals regarding finger length as destiny:

Did you know the length of your ring finger could indicate whether or not you are fertile, prone to prostate cancer or, if you are a women, likely to be a lesbian?

…men with longer ring fingers tended to be more fertile. It's the other way round for women.

…[financial] traders with longer ring fingers made more money than their short ring-fingered colleagues. They're also thought to be more aggressive, and more likely to take risks.

…lesbian women tended to have the more masculine (long ring, short index) finger arrangement.

…women with longer ring fingers did better [on spatial skills such as driving] than those whose ring fingers were equal to, or shorter than, their index fingers.

However, the latest connection with fingers seems to indicate that men whose ring fingers are longer than their index fingers are more likely to develop prostate cancer. Its conclusion is “Pattern of finger lengths may be a simple marker of prostate cancer risk, with length of 2D greater than 4D suggestive of lower risk.” However, from prostatecancerinfolink.net we learn that

the report in the British Journal of Cancer [104 (2011), 175–177. doi:10.1038/sj.bjc.6605986] is so hedged about with “mays” and “maybes” that it is unlikely to be considered definitive by too many people. We quote as follows (with bold italic type added for emphasis):

“The ratio of digit lengths is fixed in utero, and may be a proxy indicator for prenatal testosterone levels.”

Of course, on the positive side, a glance at the hand is less embarrassing than a real DRE (digital rectal exam), or a PSA [prostate specific antigen] test to look for prostate cancer. It may be as useful, at least in terms of risk. It's a lot cheaper. Of course the PSA testing companies are likely to resist this current interpretation.

Determine the typical cost of a PSA test. The PSA test is a very common screening test in the United States and much less employed in other countries such as England. What does the following graph

suggest about the efficacy of screening? Although the five-year survival rates are not shown, what does the graph suggest about five-year survival rates in the various countries? What does it suggest about finger length?

2. The three-page British Journal of Cancer study relating prostate cancer and finger length cites 19 authors plus two institutions, The UK Genetic Prostate Cancer Study Collaborators and British Association of Urological Surgeons' Section of Oncology, whose “Lists [are] available on request.” There were 1524 subjects who had prostate cancer and 3044 subjects in the control arm. Information is given for the right hand only.

Table 2. Right-hand pattern and prostate cancer risk

Finger pattern

Advanced cases (%)

Controls (%)

OR †

95% CI

P-value

Index shorter than ring

872 (57.2)

1570 (51.6)

1.00

Index equal to ring

305 (20.0)

538 (17.7)

1.05

0.88–1.25

0.580

Index longer than ring

347 (22.8)

936 (30.8)

0.67

0.57–0.80

<0.001

Total

1524 (100.0)

3044 (100.0)

Abbreviations: CI=confidence interval; OR=odds ratio.
† Adjusted for age and social class.

Unlike previous studies of finger length, finger length in this study was self-reported. Why might this be an issue?

More time in school would help?

This article suggests that the U.S. should lengthen the amount of time that children spend in school in order for its students to compete internationally in math.

[W]hen American students are competing with children around the world, who are in many cases spending four weeks longer in school each year, larking through summer is a luxury we can't afford.

Here’s the data from a printed chart that’s no longer available online. (I was not able to locate the days/hrs data online, nor any details about the nature of the statistics or the students being measured. I did find that the math scores provided match those in an OCED table[1] for 2006.)

Desk days. Although U.S. students have longer summer breaks, they spend more total hours in the classroom. Yet U.S. math scores still fall below those in many other industrialized countries

Country

Median school days (yr)

Total instructional hrs

Math scores (15-year-olds)

South Korea

204

545

547

Denmark

200

648

513

Japan

200

600

523

Mexico

200

1,047

406

Brazil

200

800

370

Australia

197

815

520

New Zealand

194

968

522

Germany

193

758

504

Norway

190

654

490

U.S.

180

1,080

474

Luxembourg

176

642

490

Spain

176

713

480

Russia

169

845

476

Italy

167

601

462

Discussion

1. For the countries shown, (a) the correlation between median days and total instructional
hours is very slightly negative (about - 0.0068), (b) the correlation between median days and math scores is slightly positive (about + 0.1083), and (c) the correlation between total instructional hours and math scores is moderately negative (about - 0.3969). Are any, or all, of these correlations surprising?
2. From this data alone, could you conclude that extending the U.S. school year or school day would improve math scores?
3. What information, behind this data, might you need in order to draw any conclusions about the effect of an extended school year or a school day on math scores in any country?
4. Which large industrialized countries are conspicuously missing from this chart?